A generalized symbolic Thomas algorithm for the solution of opposite-bordered tridiagonal linear systems

DOI10.1016/j.cam.2015.05.026zbMath1329.65066OpenAlexW642755957MaRDI QIDQ492115

Tomohiro Sogabe, Ji-Teng Jia, Su-Mei Li

Publication date: 19 August 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2015.05.026

zbMATH Keywords

determinantThomas algorithmmatrix factorizationcomputational costlinear solveropposite-bordered tridiagonal matrices

Mathematics Subject Classification ID

Factorization of matrices (15A23) Determinants, permanents, traces, other special matrix functions (15A15) Direct numerical methods for linear systems and matrix inversion (65F05) Linear difference equations (39A06)

Related Items (12)

Single step iterative method for linear system of equations with complex symmetric positive semi-definite coefficient matrices ⋮ An incomplete block-diagonalization approach for evaluating the determinants of bordered \(k\)-tridiagonal matrices ⋮ A division-free algorithm for numerically evaluating the determinant of a specific quasi-tridiagonal matrix ⋮ Numerical algorithms for the determinants of opposite-bordered and singly-bordered tridiagonal matrices ⋮ A reliable Givens-LU approach for solving opposite-bordered tridiagonal linear systems ⋮ Numerical algorithms for the determinant evaluation of general Hessenberg matrices ⋮ New algorithms for numerically solving a class of bordered tridiagonal systems of linear equations ⋮ A fast and reliable numerical solver for general bordered \(k\)-tridiagonal matrix linear equations ⋮ On determinants of cyclic pentadiagonal matrices with Toeplitz structure ⋮ A breakdown-free algorithm for computing the determinants of periodic tridiagonal matrices ⋮ An improvement of methods for solving the CUPL-Toeplitz linear system ⋮ Generalized Sherman-Morrison-Woodbury formula based algorithm for the inverses of opposite-bordered tridiagonal matrices

Uses Software

• Matlab

Cites Work

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• Inversion of \(k\)-tridiagonal matrices with Toeplitz structure
• On the eigenvalues of some tridiagonal matrices
• On a two-term recurrence for the determinant of a general matrix
• New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems
• The use of the Sherman-Morrison-Woodbury formula to solve cyclic block tri-diagonal and cyclic block penta-diagonal linear systems of equations
• Algorithms for the solution of cyclic tridiagonal systems
• A fast algorithm for evaluating \(n\)th order tri-diagonal determinants.
• Symbolic algorithm for solving comrade linear systems based on a modified stair-diagonal approach
• Inversion of general tridiagonal matrices
• Non-symbolic algorithms for the inversion of tridiagonal matrices
• Variant of the Thomas Algorithm for opposite-bordered tridiagonal systems of equations
• Matrix Analysis
• A fast numerical algorithm for solving nearly penta-diagonal linear systems
• Properties of Some Tridiagonal Matrices and Their Application to Boundary Value Problems

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